Place toor dal in a large bowl and cover by 2 inches with cool water. Using your hands, vigorously swish toor dal until water turns cloudy, about 30 seconds. Using a fine-mesh strainer, drain toor dal, discarding the cloudy water.

In a medium pot or Dutch oven, combine toor dal, 4 cups (946 ml) water, and 1 tablespoon kosher salt, and bring to a boil over high heat. Reduce heat to medium-low and simmer, skimming any foam that collects at the top, until peas are soft and break apart easily when pressed between your fingers, about 45 minutes.

Add tomato, turmeric, and 2 cups water, stirring to combine. Increase heat to medium and simmer, stirring occasionally, until the tomato has softened and completely broken down, 10 to 15 minutes.

Add Kashmiri chile powder, cayenne pepper, coconut, tamarind, and jaggery. Simmer until jaggery has completely dissolved and tamarind starts to break down, 5 to 8 minutes. The soup should be thin and watery. Remove from heat; set aside.

In a medium bowl, whisk flour, salt, turmeric, chile powder, and ajwain seeds to combine. Transfer flour mixture onto a clean work surface. Make a well in the center about 3 inches wide. Add ghee and ⅓ cup water, and using your hands or a fork, gradually incorporate flour into water until a wet, sticky dough forms.

Using a dough scraper, scrape excess dough from fingers and knead until dough feels firm and dry, and can form a craggy-looking ball, 2 to 5 minutes.

Press the heel of your hand into the ball of dough, pushing forward and down. Rotate the ball 45° and repeat. Continue until dough develops a smooth, elastic texture similar to a firm ball of Play-Doh. If dough feels too wet, add flour in 1 teaspoon increments. If dough feels too dry, add water slowly using a spray bottle.

Wrap ball of dough tightly in plastic wrap and rest at room temperature for 30 minutes.

Place a sheet of parchment paper on a tray or cutting board and dust lightly with flour. Unwrap rested dough and cut into quarters. Set one quarter on work surface and re-wrap remaining dough. With a rolling pin, flatten the quarter of dough into an oblong shape about ½ inch thick.

Set pasta maker to widest setting and pass dough 3 times through the machine at this setting. Place dough on a lightly floured work surface. Fold both ends in so that they meet at the center of the dough, and then fold the dough in half where the end points meet. Using a rolling pin, flatten dough to ½-inch thick. Pass through the rollers 3 additional times.

Narrow the setting by 1 notch and repeat. Continue passing the dough through the rollers, reducing the thickness by 1 setting each time until delicate and elastic to the touch, and slightly translucent.

Place rolled dough onto a work surface lightly dusted with flour; sprinkle dough with flour as necessary to prevent sticking. Using a pizza cutter or knife, cut dough into 40 to 50 1 ½- to 2-inch squares or diamonds. Line a rimmed 13-by-18-inch baking sheet with parchment and lightly dust with flour. Transfer prepared pasta to baking sheet.

Bring the dal to a rolling boil. If dal has thickened slightly and is no longer watery, add up to 1 cup water to thin out. Gently drop the dhokli into the dal a few at a time, stirring as needed to prevent them from sticking, until all dhokli is in the pot. Cook dhokli until they start to float to top and are al dente in texture, 6 to 8 minutes. Season dal to taste, then add cilantro and stir to combine. Remove from heat; set aside.

In a small bowl, combine asafoetida, mustard seeds, cumin seeds, fenugreek seeds, and cloves. In small saucepan or skillet, heat ghee over high heat until it just begins to smoke. Reduce heat to medium, and carefully add asafoetida, mustard seeds, cumin seeds, fenugreek seeds, and cloves. Cook, allowing seeds to sizzle and pop, 10 to 15 seconds. Add bay leaf and cook, stirring constantly, until it sizzles, about 5 seconds more. Immediately pour tadka over daal and stir to incorporate.